Coursera Flash Sale
40% Off Coursera Plus for 3 Months!
Grab it
This lecture is the third part of a series exploring the Berezinskii-Kosterlitz-Thouless (BKT) phase transition in statistical physics, presented by Christophe Garban at the Hausdorff Center for Mathematics. Delve into the fascinating world of spin systems on lattices and how they fluctuate with temperature changes. Understand the fundamental differences between discrete spin systems (like the Ising model) and continuous spin systems (such as the XY model with unit circle S¹ spins or the classical Heisenberg model with unit sphere S² spins). Explore how continuous symmetry systems exhibit drastically different phase transition behaviors compared to discrete symmetry settings, with special focus on the BKT phase transition predicted in the 1970s. Learn about the role of "vortices" (special monodromies) in triggering this unique phase transition in two-dimensional systems. Discover the key ideas behind recent mathematical proofs confirming the existence of this transition and examine the latest research developments in this field during this hour-long advanced physics lecture.
